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Sa se rezolve ecuatia:

[tex] \frac{5}{x+m}- \frac{1}{m-x}=2+ \frac{10m}{m^2-x^2} [/tex]

Mersi.


Răspuns :

[tex] \frac{5m-5x-x-m}{ m^{2}- x^{2} }= \frac{2 m^{2}-2 x^{2} +10m }{ m^{2}- x^{2} } \\ 4m-6x=2 m^{2}-2x^2+10m \\ 2x^2-6x-2m^2-6m=0 \\ x^{2} -3x-m^2-3=0[/tex]
Δ=9+4(m^2+3)=4m^2+21
[tex] x_{1} = \frac{3- \sqrt{4m^2+21} }{2} \\ x_{2}= \frac{3+ \sqrt{4m^2+21} }{2} [/tex]